What This Document Is
This document is a note sheet prepared for students in Duke University’s Probability course (STA 230), specifically Section 2. It consolidates key formulas, theorems, and statistical distributions covered throughout the course, intended as a study aid for a final exam. It’s a quick-reference resource, not a comprehensive textbook replacement.
Why This Document Matters
This note sheet is valuable for students preparing for the final exam in STA 230. It provides a centralized location for essential probability concepts and mathematical expressions, saving time during review. It’s particularly useful for students who need a refresher on specific distributions or formulas before tackling practice problems or the exam itself. It’s designed to be used *in conjunction with* course materials, not as a standalone study tool.
Common Limitations or Challenges
This note sheet is a condensed summary. It does not include detailed explanations of the concepts, derivations of the formulas, or illustrative examples. It assumes a foundational understanding of probability theory developed throughout the course. It won’t teach you the material; it only helps you recall what you’ve already learned.
What This Document Provides
The full note sheet includes:
* A listing of common discrete probability distributions (Uniform, Bernoulli, Binomial, Poisson, Hypergeometric, Geometric) with their probability mass functions.
* A listing of common continuous probability distributions (Uniform, Exponential, Gamma) with their probability density functions and cumulative distribution functions.
* Formulas for calculating expectations and variances for both discrete and continuous random variables.
* Key theorems, including Markov’s Inequality, Chebyshev’s Inequality, the Weak Law of Large Numbers, and the Central Limit Theorem.
* Formulas for marginal and conditional probability.
* Identities related to covariance and variance.
* Infinite sum formulas.
* A standard normal distribution table (Z-table) for calculating probabilities.
This preview does *not* include the full Z-table, detailed explanations of the theorems, or worked examples of how to apply the formulas.